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Based on unit feedback closed-loop control structure, a simple analytical design method of decoupling controller matrix is proposed in terms of idea of coupling matrix for two-input-two-output (TITO) processes with time delays in chemical and industrial practice. By means of powerful robustness of two degree-of-freedom PID Desired Dynamic Equation (DDE) method, PID decoupling controller is analytically designed. And the Monte-Carlo stochastic experiment is introduced to analyze performance robustness of the controller. The most important merit of the proposed method is that for the nominal system the output of each channel can be decoupled entirely. Moreover, the decoupling matrix is simple and easily realized. Finally, illustrative simulation examples are included to demonstrate the remarkable superiority of the proposed method

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In this paper, a practical passivity-based control (PBC) with active disturbance rejection control (ADRC) is proposed to improve performance of the Vienna rectifier under unbalanced grid conditions. In general, the traditional double-loop control based on positive and negative sequence transformation is used in Vienna rectifier under unbalanced grid conditions. However, it could not fundamentally solve the additional time delay caused by the second harmonic filter and loss of performance caused by a linear weighted sum of proportional integral (PI) controller. What's more, the complexity of the controller is high for the positive and negative sequence currents need to be controlled separately. The PBC is a nonlinear controller based on energy dissipation and it has strong robustness to interference. Further, the line voltage based PBC in inner current loop can deal with the voltage unbalance effectively and easily without negative sequence transformation. To improve the disturbance rejection ability, the ADRC is applied in outer voltage loop, which could overcome PI's drawbacks of step overshoot and slow response. Under unbalanced grid conditions, the proposed control strategy has good performance, easy implementation and less consuming time with PBC control in inner current loop, and it has strong robustness and fast track performance with ADRC control in outer voltage loop. The detailed mathematical model, control principle and controller design of the Vienna rectifier are thoroughly analyzed. In addition, simulation results based on SIMULINK are also given in the paper. Finally, a downsize 5kW Vienna rectifier prototype is built to validate the correctness and effectiveness of the proposed strategy. INDEX TERMS Active disturbance rejection control, passivity-based control, unbalanced grid condition, Vienna rectifier.